Exercise 59 Page 86

To solve the equation, we have to isolate r on one side. We will start by rewriting the mixed number as an improper fraction. Then, we will use the Multiplication Property of Equality and multiply both sides of the equation by 5. This will eliminate the denominator of the fraction and isolate r. Therefore, r= 1254 is the solution to the equation. To check that we have the correct solution, we can substitute r= 1254 into the original equation and simplify.

6 14? =r/5

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Write mixed number as a fraction

MixedToFrac

a bc=a* c+b/c

6*4+1/4? =r/5

Multiply

Multiply

24+1/4? =r/5

AddTerms

Add terms

25/4? =r/5

Substitute

r= 125/4

25/4? =. 125/4 /5.

DivFracSL

.a/b /c.= a/b* c

25/4? =125/4*5

Multiply

Multiply

25/4? =125/20

ReduceFrac

a/b=.a /5./.b /5.

25/4? =125/5/20/5

CalcQuot

Calculate quotient

25/4=25/4 ✓

Since the left-hand side and the right-hand side are equal, r= 1254 is the correct solution. However, we can also write our answer as a mixed number.

r=125/4

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Write as mixed number

Rewrite

Rewrite 125 as 124+1

r=124+1/4

WriteSumFrac

Write as a sum of fractions

r=124/4+1/4

CalcQuot

Calculate quotient

r=31+1/4

Finally, the numeric expression 31+ 14 can be read as 31 and 14. Therefore, it can be written as 31 14. y=31+1/4 ⇔ y=31 14